Download today`s handout - Algebra with Mrs. Jett!

Name ____________________________
Linear Regression
The __________________________________________________ is the line that lies as
close as possible to all the data points.
______________________________________________ is a method used to find the
equation of the best fitting line or curve.
Approximating a Best-Fitting Line (By Hand)
STEP 1 Draw a scatter plot of the data.
STEP 2 Sketch the line that appears to follow most closely the trend given by the data
points. There should be about as many points above the line as below it.
STEP 3 Choose two points on the line, and estimate the coordinates of each point. These
points do not have to be original data points. Find the slope of these two points.
Slope formula:
STEP 4 Find the y-intercept of your line of best fit by solving for b.
STEP 5 Write an equation of the line you drew using your slope and y-intercept.
Line of Best Fit: Calculator
FIRST: Set your window to match your data!
STEP 1
Stat/Enter
STEP 2
Clear List 1 & List 2 (Select the List # at the top, then Clear/Enter.
STEP 3
Enter your data into List 1 (x) and List 2 (y).
STEP 4
Stat/Calc/4:LinReg (ax + b)
STEP 5
Write the equation in slope-intercept form: y = ax + b
To Make a Scatter Plot on the Calculator
STEP 1
STEP 2
2nd/Stat Plot/Enter/On/Type: 1st/X-List: L1/Y-List: L2
Graph
STEP 1
STEP 2
To See your LOBF over your Scatter Plot
Y= and put in your LOBF equation
Graph
1. The table shows the number y (in thousands) of alternative-fueled vehicles in use in the
United States x years after 1997. Calculate the best-fitting line for the data.
x
0
1
2
3
4
5
6
7
y
280
295
322
395
425
471
511
548
Use the graphing calculator to find the actual line of best fit (the linear regression line).
y = _____________________________________
Use this equation to predict the number of vehicles in 2020. ___________________________
Interpret the slope and y-intercept of the equation.
What is the r value on the calculator for this line of best fit? _____________
This is the correlation coefficient; it helps you assess the accuracy of your LOBF.
2. This table shown displays the number of total number of fat grams and total calories in types of
drinks.
Total
Fat (g)
3
7
2
6
6
10
Total
Calories
21
58
13
45
56
87
a) Enter your data in the calculator and make the scatter plot.
b) Find the actual line of best fit (Stat/Calc/LinReg#4). y = ________________________________________________
c) Round the correlation coefficient (r) to the nearest ten thousandth. _____________________________
d) Strength and Direction according to r? ________________________________________________
e) Use the equation to predict the number of calories in a drink with 15 fat grams. _____________________
3. Use the table below to answer the questions about the operating costs in thousands of a small
business from 2000 to 2007.
Year, t
Operating
2000
2001
2002
2003
2004
2005
2006
2007
2.3
2.6
3.1
3.3
4.0
5.2
5.9
7.0
Costs
a) Find the best-fitting line for the data. y = ________________________________________________
b) Round the correlation coefficient (r) to the nearest ten thousandth. _____________________________
c) Strength and Direction according to r? ________________________________________________
d) Using this model, what will the operating costs be in 2015? ________________________________________________
4.
Enter your data.
Create a scatter plot.
Find the Line of Best Fit. y = ____________________________________________________________________________
A Whopper has 37 grams of fat. Use your equation to predict the number of calories in a whopper.
Use your equation to predict the number of fat grams in a large serving of McDonald’s fries if they have 510
calories.